The scattering of sound waves by an empty, cylindrical, elastic shell in a fluid is considered in the resonance regime. A long-standing difficulty in the application of the resonance scattering theory is that an exact expression of the acoustical background has been elusive to find over the years. The exact expression, named theinherentbackground coefficient, is presented here. The coefficient is uniquely determined by the generalized fluid-loading-parameter and leads to the impenetrable background coefficient in appropriate limit. Numerical calculations show that it describes the background for a shell of arbitrary thickness and material correctly over the entire frequency range.